Analytic computations for decay rate of blackhole perturbations have been carried out in the BTZ background in [1]}. The BTZ blackhole metric is a solution of vacuum Einstein field equations in three dimensions with negative cosmological constant, \(\lambda =-1/L^{2}\)  [2]} where \(L\)  is the radius of curvature of the space-time. The exact computation of the BTZ blackhole probed by a mass-less scalar field yields the following decay rate
\(\Gamma ^{(\text{decay})} \propto e^{-\frac{\omega }{2T_{H}}} \omega ^{-1} T_{H} \bigg \vert \Gamma \left( 1 + i \frac{\omega }{4\pi T_{L}} \right) \Gamma \left(1+i\frac{\omega }{4\pi T_{R}}\right)\bigg \vert ^2,\) 
